Explanation Given information: The demand equation for a quantity q of a product at price p, in dollars is p = − 5 q + 4000 . The cost to produce the quantity q is C = 6 q + 5 dollars. Formulas used: The profit π ( q ) is the difference between the revenue, R ( q ) , and the cost, C ( q ) , of supplying that quantity. ⇒ π ( q ) = R ( q ) − C ( q ) The revenue is given by R = q . p , where q is the quantity and p is the price of the product. Calculation: p = − 5 q + 4000 and C = 6 q + 5 (Given) The profit is π ( q ) = R ( q ) − C ( q ) ⇒ π ( q ) = q To determine (b) To find: The largest profit. To determine (c) To find: The largest profit.

6th Edition

ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 4.4, Problem 24P

To determine

(a)

To express:

The company profit, in dollars, as a function of q.

To determine

(b)

To find:

The largest profit.

To determine

(c)

To find:

The largest profit.

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Chapter 4.4, Problem 23P

Chapter 4.4, Problem 25P

Chapter 4 Solutions

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(a) To express: The company profit, in dollars, as a function of q.

Solution Summary: The author explains that the company profit is denoted by a function q as pi (q)=-5+3994q-5q2.

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(a) To express: The company profit, in dollars, as a function of q.

(b) To find: The largest profit.

(c) To find: The largest profit.

Want to see the full answer?

Chapter 4 Solutions

(a)

To express:

The company profit, in dollars, as a function of q.

(b)

To find:

The largest profit.

(c)

To find:

The largest profit.